LMFDB - Embedded newform 104.2.b.c.53.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(53,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.5
Root			$-0.671462 + 1.24464i$ of defining polynomial
Character	$\chi$	$=$	104.53
Dual form			104.2.b.c.53.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.671462 - 1.24464i) q^{2} -0.146365i q^{3} +(-1.09828 - 1.67146i) q^{4} -1.00000i q^{5} +(-0.182173 - 0.0982788i) q^{6} -0.146365 q^{7} +(-2.81783 + 0.244644i) q^{8} +2.97858 q^{9} +(-1.24464 - 0.671462i) q^{10} +2.68585i q^{11} +(-0.244644 + 0.160750i) q^{12} +1.00000i q^{13} +(-0.0982788 + 0.182173i) q^{14} -0.146365 q^{15} +(-1.58757 + 3.67146i) q^{16} +1.00000 q^{17} +(2.00000 - 3.70727i) q^{18} +4.00000i q^{19} +(-1.67146 + 1.09828i) q^{20} +0.0214229i q^{21} +(3.34292 + 1.80344i) q^{22} -6.68585 q^{23} +(0.0358075 + 0.412433i) q^{24} +4.00000 q^{25} +(1.24464 + 0.671462i) q^{26} -0.875057i q^{27} +(0.160750 + 0.244644i) q^{28} -4.39312i q^{29} +(-0.0982788 + 0.182173i) q^{30} +1.31415 q^{31} +(3.50367 + 4.44120i) q^{32} +0.393115 q^{33} +(0.671462 - 1.24464i) q^{34} +0.146365i q^{35} +(-3.27131 - 4.97858i) q^{36} +3.97858i q^{37} +(4.97858 + 2.68585i) q^{38} +0.146365 q^{39} +(0.244644 + 2.81783i) q^{40} -6.39312 q^{41} +(0.0266638 + 0.0143846i) q^{42} -6.83221i q^{43} +(4.48929 - 2.94981i) q^{44} -2.97858i q^{45} +(-4.48929 + 8.32150i) q^{46} -7.12494 q^{47} +(0.537375 + 0.232365i) q^{48} -6.97858 q^{49} +(2.68585 - 4.97858i) q^{50} -0.146365i q^{51} +(1.67146 - 1.09828i) q^{52} -8.97858i q^{53} +(-1.08914 - 0.587567i) q^{54} +2.68585 q^{55} +(0.412433 - 0.0358075i) q^{56} +0.585462 q^{57} +(-5.46787 - 2.94981i) q^{58} -12.3503i q^{59} +(0.160750 + 0.244644i) q^{60} +8.35027i q^{61} +(0.882404 - 1.63565i) q^{62} -0.435961 q^{63} +(7.88030 - 1.37873i) q^{64} +1.00000 q^{65} +(0.263962 - 0.489289i) q^{66} +8.29273i q^{67} +(-1.09828 - 1.67146i) q^{68} +0.978577i q^{69} +(0.182173 + 0.0982788i) q^{70} +5.51806 q^{71} +(-8.39312 + 0.728692i) q^{72} -6.97858 q^{73} +(4.95191 + 2.67146i) q^{74} -0.585462i q^{75} +(6.68585 - 4.39312i) q^{76} -0.393115i q^{77} +(0.0982788 - 0.182173i) q^{78} +15.0361 q^{79} +(3.67146 + 1.58757i) q^{80} +8.80765 q^{81} +(-4.29273 + 7.95715i) q^{82} +4.29273i q^{83} +(0.0358075 - 0.0235283i) q^{84} -1.00000i q^{85} +(-8.50367 - 4.58757i) q^{86} -0.643000 q^{87} +(-0.657077 - 7.56825i) q^{88} -5.37169 q^{89} +(-3.70727 - 2.00000i) q^{90} -0.146365i q^{91} +(7.34292 + 11.1751i) q^{92} -0.192347i q^{93} +(-4.78412 + 8.86802i) q^{94} +4.00000 q^{95} +(0.650039 - 0.512817i) q^{96} -10.3503 q^{97} +(-4.68585 + 8.68585i) q^{98} +8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} - 10 q^{6} + 2 q^{7} - 8 q^{8} - 12 q^{9} + 6 q^{12} + 4 q^{14} + 2 q^{15} + 10 q^{16} + 6 q^{17} + 12 q^{18} - 4 q^{20} + 8 q^{22} - 16 q^{23} + 12 q^{24} + 24 q^{25} - 20 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 - 10 * q^6 + 2 * q^7 - 8 * q^8 - 12 * q^9 + 6 * q^12 + 4 * q^14 + 2 * q^15 + 10 * q^16 + 6 * q^17 + 12 * q^18 - 4 * q^20 + 8 * q^22 - 16 * q^23 + 12 * q^24 + 24 * q^25 - 20 * q^28 + 4 * q^30 + 32 * q^31 - 12 * q^32 - 16 * q^33 - 2 * q^34 + 16 * q^36 - 2 * q^39 - 6 * q^40 - 20 * q^41 - 28 * q^42 + 12 * q^44 - 12 * q^46 - 10 * q^47 - 10 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 + 38 * q^54 - 8 * q^55 + 22 * q^56 - 8 * q^57 + 12 * q^58 - 20 * q^60 - 28 * q^62 - 44 * q^63 + 22 * q^64 + 6 * q^65 + 32 * q^66 - 2 * q^68 + 10 * q^70 - 18 * q^71 - 32 * q^72 - 12 * q^73 + 28 * q^74 + 16 * q^76 - 4 * q^78 - 12 * q^79 + 16 * q^80 + 46 * q^81 - 20 * q^82 + 12 * q^84 - 18 * q^86 + 80 * q^87 - 16 * q^88 + 16 * q^89 - 28 * q^90 + 32 * q^92 + 24 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.671462	−	1.24464i	0.474795	−	0.880096i
$2$	0.671462	−	1.24464i	0.474795	−	0.880096i
$3$		−	0.146365i		−	0.0845042i	−0.999107	−	0.0422521i	$-0.986547\pi$
$3$		−	0.146365i		−	0.0845042i	0.999107	−	0.0422521i	$-0.0134533\pi$
$4$	−1.09828	−	1.67146i	−0.549139	−	0.835731i
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$	−0.182173	−	0.0982788i	−0.0743718	−	0.0401222i
$7$	−0.146365			−0.0553210			−0.0276605	−	0.999617i	$-0.508806\pi$
$7$	−0.146365			−0.0553210			−0.0276605	+	0.999617i	$0.508806\pi$
$8$	−2.81783	+	0.244644i	−0.996252	+	0.0864948i
$9$	2.97858			0.992859
$10$	−1.24464	−	0.671462i	−0.393591	−	0.212335i
$11$			2.68585i			0.809813i	0.914358	+	0.404907i	$0.132696\pi$
$11$			2.68585i			0.809813i	−0.914358	+	0.404907i	$0.867304\pi$
$12$	−0.244644	+	0.160750i	−0.0706227	+	0.0464046i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−0.0982788	+	0.182173i	−0.0262661	+	0.0486878i
$15$	−0.146365			−0.0377914
$16$	−1.58757	+	3.67146i	−0.396892	+	0.917865i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$	2.00000	−	3.70727i	0.471405	−	0.873812i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−1.67146	+	1.09828i	−0.373750	+	0.245583i
$21$			0.0214229i			0.00467485i
$22$	3.34292	+	1.80344i	0.712714	+	0.384495i
$23$	−6.68585			−1.39410			−0.697048	−	0.717025i	$-0.745503\pi$
$23$	−6.68585			−1.39410			−0.697048	+	0.717025i	$0.745503\pi$
$24$	0.0358075	+	0.412433i	0.00730917	+	0.0841875i
$25$	4.00000			0.800000
$26$	1.24464	+	0.671462i	0.244095	+	0.131684i
$27$		−	0.875057i		−	0.168405i
$28$	0.160750	+	0.244644i	0.0303789	+	0.0462334i
$29$		−	4.39312i		−	0.815781i	−0.913031	−	0.407891i	$-0.866265\pi$
$29$		−	4.39312i		−	0.815781i	0.913031	−	0.407891i	$-0.133735\pi$
$30$	−0.0982788	+	0.182173i	−0.0179432	+	0.0332601i
$31$	1.31415			0.236029			0.118014	−	0.993012i	$-0.462347\pi$
$31$	1.31415			0.236029			0.118014	+	0.993012i	$0.462347\pi$
$32$	3.50367	+	4.44120i	0.619368	+	0.785101i
$33$	0.393115			0.0684326
$34$	0.671462	−	1.24464i	0.115155	−	0.213455i
$35$			0.146365i			0.0247403i
$36$	−3.27131	−	4.97858i	−0.545218	−	0.829763i
$37$			3.97858i			0.654074i	0.945012	+	0.327037i	$0.106050\pi$
$37$			3.97858i			0.654074i	−0.945012	+	0.327037i	$0.893950\pi$
$38$	4.97858	+	2.68585i	0.807632	+	0.435702i
$39$	0.146365			0.0234372
$40$	0.244644	+	2.81783i	0.0386817	+	0.445538i
$41$	−6.39312			−0.998437			−0.499218	−	0.866476i	$-0.666379\pi$
$41$	−6.39312			−0.998437			−0.499218	+	0.866476i	$0.666379\pi$
$42$	0.0266638	+	0.0143846i	0.00411432	+	0.00221960i
$43$		−	6.83221i		−	1.04190i	−0.853586	−	0.520951i	$-0.825577\pi$
$43$		−	6.83221i		−	1.04190i	0.853586	−	0.520951i	$-0.174423\pi$
$44$	4.48929	−	2.94981i	0.676786	−	0.444700i
$45$		−	2.97858i		−	0.444020i
$46$	−4.48929	+	8.32150i	−0.661909	+	1.22694i
$47$	−7.12494			−1.03928			−0.519640	−	0.854385i	$-0.673934\pi$
$47$	−7.12494			−1.03928			−0.519640	+	0.854385i	$0.673934\pi$
$48$	0.537375	+	0.232365i	0.0775634	+	0.0335390i
$49$	−6.97858			−0.996940
$50$	2.68585	−	4.97858i	0.379836	−	0.704077i
$51$		−	0.146365i		−	0.0204953i
$52$	1.67146	−	1.09828i	0.231790	−	0.152304i
$53$		−	8.97858i		−	1.23330i	−0.787236	−	0.616651i	$-0.788489\pi$
$53$		−	8.97858i		−	1.23330i	0.787236	−	0.616651i	$-0.211511\pi$
$54$	−1.08914	−	0.587567i	−0.148213	−	0.0799578i
$55$	2.68585			0.362159
$56$	0.412433	−	0.0358075i	0.0551136	−	0.00478498i
$57$	0.585462			0.0775463
$58$	−5.46787	−	2.94981i	−0.717966	−	0.387329i
$59$		−	12.3503i		−	1.60787i	−0.594718	−	0.803934i	$-0.702736\pi$
$59$		−	12.3503i		−	1.60787i	0.594718	−	0.803934i	$-0.297264\pi$
$60$	0.160750	+	0.244644i	0.0207528	+	0.0315834i
$61$			8.35027i			1.06914i	0.845123	+	0.534571i	$0.179527\pi$
$61$			8.35027i			1.06914i	−0.845123	+	0.534571i	$0.820473\pi$
$62$	0.882404	−	1.63565i	0.112065	−	0.207728i
$63$	−0.435961			−0.0549259
$64$	7.88030	−	1.37873i	0.985037	−	0.172341i
$65$	1.00000			0.124035
$66$	0.263962	−	0.489289i	0.0324914	−	0.0602273i
$67$			8.29273i			1.01312i	0.862205	+	0.506559i	$0.169083\pi$
$67$			8.29273i			1.01312i	−0.862205	+	0.506559i	$0.830917\pi$
$68$	−1.09828	−	1.67146i	−0.133186	−	0.202694i
$69$			0.978577i			0.117807i
$70$	0.182173	+	0.0982788i	0.0217738	+	0.0117466i
$71$	5.51806			0.654873			0.327436	−	0.944873i	$-0.393815\pi$
$71$	5.51806			0.654873			0.327436	+	0.944873i	$0.393815\pi$
$72$	−8.39312	+	0.728692i	−0.989138	+	0.0858772i
$73$	−6.97858			−0.816781			−0.408390	−	0.912807i	$-0.633910\pi$
$73$	−6.97858			−0.816781			−0.408390	+	0.912807i	$0.633910\pi$
$74$	4.95191	+	2.67146i	0.575648	+	0.310551i
$75$		−	0.585462i		−	0.0676033i
$76$	6.68585	−	4.39312i	0.766919	−	0.503925i
$77$		−	0.393115i		−	0.0447996i
$78$	0.0982788	−	0.182173i	0.0111279	−	0.0206270i
$79$	15.0361			1.69170			0.845848	−	0.533425i	$-0.179095\pi$
$79$	15.0361			1.69170			0.845848	+	0.533425i	$0.179095\pi$
$80$	3.67146	+	1.58757i	0.410482	+	0.177495i
$81$	8.80765			0.978628
$82$	−4.29273	+	7.95715i	−0.474053	+	0.878721i
$83$			4.29273i			0.471188i	0.971852	+	0.235594i	$0.0757036\pi$
$83$			4.29273i			0.471188i	−0.971852	+	0.235594i	$0.924296\pi$
$84$	0.0358075	−	0.0235283i	0.00390692	−	0.00256714i
$85$		−	1.00000i		−	0.108465i
$86$	−8.50367	−	4.58757i	−0.916975	−	0.494690i
$87$	−0.643000			−0.0689369
$88$	−0.657077	−	7.56825i	−0.0700446	−	0.806778i
$89$	−5.37169			−0.569398			−0.284699	−	0.958617i	$-0.591894\pi$
$89$	−5.37169			−0.569398			−0.284699	+	0.958617i	$0.591894\pi$
$90$	−3.70727	−	2.00000i	−0.390780	−	0.210819i
$91$		−	0.146365i		−	0.0153433i
$92$	7.34292	+	11.1751i	0.765553	+	1.16509i
$93$		−	0.192347i		−	0.0199454i
$94$	−4.78412	+	8.86802i	−0.493445	+	0.914666i
$95$	4.00000			0.410391
$96$	0.650039	−	0.512817i	0.0663443	−	0.0523391i
$97$	−10.3503			−1.05091			−0.525455	−	0.850821i	$-0.676105\pi$
$97$	−10.3503			−1.05091			−0.525455	+	0.850821i	$0.676105\pi$
$98$	−4.68585	+	8.68585i	−0.473342	+	0.877403i
$99$			8.00000i			0.804030i
$100$	−4.39312	−	6.68585i	−0.439312	−	0.668585i
$101$			17.9572i			1.78680i	0.449258	+	0.893402i	$0.351688\pi$
$101$			17.9572i			1.78680i	−0.449258	+	0.893402i	$0.648312\pi$
$102$	−0.182173	−	0.0982788i	−0.0180378	−	0.00973105i
$103$	10.2499			1.00995			0.504976	−	0.863134i	$-0.331501\pi$
$103$	10.2499			1.00995			0.504976	+	0.863134i	$0.331501\pi$
$104$	−0.244644	−	2.81783i	−0.0239893	−	0.276311i
$105$	0.0214229			0.00209066
$106$	−11.1751	−	6.02877i	−1.08543	−	0.585566i
$107$		−	14.6858i		−	1.41973i	−0.704336	−	0.709867i	$-0.748755\pi$
$107$		−	14.6858i		−	1.41973i	0.704336	−	0.709867i	$-0.251245\pi$
$108$	−1.46262	+	0.961057i	−0.140741	+	0.0924777i
$109$			14.7648i			1.41421i	0.707108	+	0.707106i	$0.250000\pi$
$109$			14.7648i			1.41421i	−0.707108	+	0.707106i	$0.750000\pi$
$110$	1.80344	−	3.34292i	0.171951	−	0.318735i
$111$	0.582326			0.0552720
$112$	0.232365	−	0.537375i	0.0219564	−	0.0507772i
$113$	3.95715			0.372258			0.186129	−	0.982525i	$-0.440406\pi$
$113$	3.95715			0.372258			0.186129	+	0.982525i	$0.440406\pi$
$114$	0.393115	−	0.728692i	0.0368186	−	0.0682482i
$115$			6.68585i			0.623458i
$116$	−7.34292	+	4.82487i	−0.681773	+	0.447977i
$117$			2.97858i			0.275370i
$118$	−15.3717	−	8.29273i	−1.41508	−	0.763408i
$119$	−0.146365			−0.0134173
$120$	0.412433	−	0.0358075i	0.0376498	−	0.00326876i
$121$	3.78623			0.344203
$122$	10.3931	+	5.60688i	0.940948	+	0.507623i
$123$			0.935731i			0.0843721i
$124$	−1.44331	−	2.19656i	−0.129613	−	0.197257i
$125$		−	9.00000i		−	0.804984i
$126$	−0.292731	+	0.542616i	−0.0260785	+	0.0483401i
$127$	−6.10038			−0.541322			−0.270661	−	0.962675i	$-0.587242\pi$
$127$	−6.10038			−0.541322			−0.270661	+	0.962675i	$0.587242\pi$
$128$	3.57529	−	10.7339i	0.316014	−	0.948755i
$129$	−1.00000			−0.0880451
$130$	0.671462	−	1.24464i	0.0588911	−	0.109163i
$131$			14.8322i			1.29590i	0.761684	+	0.647948i	$0.224373\pi$
$131$			14.8322i			1.29590i	−0.761684	+	0.647948i	$0.775627\pi$
$132$	−0.431750	−	0.657077i	−0.0375790	−	0.0571912i
$133$		−	0.585462i		−	0.0507660i
$134$	10.3215	+	5.56825i	0.891642	+	0.481024i
$135$	−0.875057			−0.0753129
$136$	−2.81783	+	0.244644i	−0.241627	+	0.0209781i
$137$	9.76481			0.834264			0.417132	−	0.908846i	$-0.363035\pi$
$137$	9.76481			0.834264			0.417132	+	0.908846i	$0.363035\pi$
$138$	1.21798	+	0.657077i	0.103681	+	0.0559341i
$139$		−	19.4752i		−	1.65187i	−0.563768	−	0.825933i	$-0.690649\pi$
$139$		−	19.4752i		−	1.65187i	0.563768	−	0.825933i	$-0.309351\pi$
$140$	0.244644	−	0.160750i	0.0206762	−	0.0135859i
$141$			1.04285i			0.0878235i
$142$	3.70516	−	6.86802i	0.310930	−	0.576351i
$143$	−2.68585			−0.224602
$144$	−4.72869	+	10.9357i	−0.394058	+	0.911311i
$145$	−4.39312			−0.364828
$146$	−4.68585	+	8.68585i	−0.387803	+	0.718846i
$147$			1.02142i			0.0842455i
$148$	6.65004	−	4.36959i	0.546630	−	0.359178i
$149$		−	11.9572i		−	0.979568i	−0.871844	−	0.489784i	$-0.837076\pi$
$149$		−	11.9572i		−	0.979568i	0.871844	−	0.489784i	$-0.162924\pi$
$150$	−0.728692	−	0.393115i	−0.0594974	−	0.0320977i
$151$	12.7894			1.04078			0.520392	−	0.853928i	$-0.325786\pi$
$151$	12.7894			1.04078			0.520392	+	0.853928i	$0.325786\pi$
$152$	−0.978577	−	11.2713i	−0.0793731	−	0.914224i
$153$	2.97858			0.240804
$154$	−0.489289	−	0.263962i	−0.0394280	−	0.0212706i
$155$		−	1.31415i		−	0.105555i
$156$	−0.160750	−	0.244644i	−0.0128703	−	0.0195872i
$157$		−	21.7220i		−	1.73360i	−0.498655	−	0.866801i	$-0.666172\pi$
$157$		−	21.7220i		−	1.73360i	0.498655	−	0.866801i	$-0.333828\pi$
$158$	10.0962	−	18.7146i	0.803208	−	1.48885i
$159$	−1.31415			−0.104219
$160$	4.44120	−	3.50367i	0.351108	−	0.276990i
$161$	0.978577			0.0771227
$162$	5.91400	−	10.9624i	0.464648	−	0.861287i
$163$		−	20.6430i		−	1.61688i	−0.588575	−	0.808442i	$-0.700311\pi$
$163$		−	20.6430i		−	1.61688i	0.588575	−	0.808442i	$-0.299689\pi$
$164$	7.02142	+	10.6858i	0.548281	+	0.834424i
$165$		−	0.393115i		−	0.0306040i
$166$	5.34292	+	2.88240i	0.414691	+	0.223718i
$167$	−18.0147			−1.39402			−0.697009	−	0.717062i	$-0.745486\pi$
$167$	−18.0147			−1.39402			−0.697009	+	0.717062i	$0.745486\pi$
$168$	−0.00524098	−	0.0603659i	−0.000404350	−	0.00465733i
$169$	−1.00000			−0.0769231
$170$	−1.24464	−	0.671462i	−0.0954599	−	0.0514987i
$171$			11.9143i			0.911110i
$172$	−11.4198	+	7.50367i	−0.870750	+	0.572150i
$173$			6.58546i			0.500683i	0.968158	+	0.250342i	$0.0805430\pi$
$173$			6.58546i			0.500683i	−0.968158	+	0.250342i	$0.919457\pi$
$174$	−0.431750	+	0.800307i	−0.0327309	+	0.0606711i
$175$	−0.585462			−0.0442568
$176$	−9.86098	−	4.26396i	−0.743299	−	0.321408i
$177$	−1.80765			−0.135872
$178$	−3.60688	+	6.68585i	−0.270347	+	0.501125i
$179$			7.56090i			0.565128i	0.959248	+	0.282564i	$0.0911850\pi$
$179$			7.56090i			0.565128i	−0.959248	+	0.282564i	$0.908815\pi$
$180$	−4.97858	+	3.27131i	−0.371081	+	0.243829i
$181$		−	0.628308i		−	0.0467017i	−0.999727	−	0.0233509i	$-0.992567\pi$
$181$		−	0.628308i		−	0.0467017i	0.999727	−	0.0233509i	$-0.00743349\pi$
$182$	−0.182173	−	0.0982788i	−0.0135036	−	0.00728491i
$183$	1.22219			0.0903470
$184$	18.8396	−	1.63565i	1.38887	−	0.120582i
$185$	3.97858			0.292511
$186$	−0.239403	−	0.129153i	−0.0175539	−	0.00946999i
$187$			2.68585i			0.196409i
$188$	7.82517	+	11.9091i	0.570709	+	0.868558i
$189$			0.128078i			0.00931632i
$190$	2.68585	−	4.97858i	0.194852	−	0.361184i
$191$	−10.1004			−0.730838			−0.365419	−	0.930843i	$-0.619074\pi$
$191$	−10.1004			−0.730838			−0.365419	+	0.930843i	$0.619074\pi$
$192$	−0.201799	−	1.15340i	−0.0145636	−	0.0832397i
$193$	−3.37169			−0.242700			−0.121350	−	0.992610i	$-0.538722\pi$
$193$	−3.37169			−0.242700			−0.121350	+	0.992610i	$0.538722\pi$
$194$	−6.94981	+	12.8824i	−0.498967	+	0.924903i
$195$		−	0.146365i		−	0.0104815i
$196$	7.66442	+	11.6644i	0.547459	+	0.833173i
$197$		−	14.7220i		−	1.04890i	−0.851442	−	0.524448i	$-0.824272\pi$
$197$		−	14.7220i		−	1.04890i	0.851442	−	0.524448i	$-0.175728\pi$
$198$	9.95715	+	5.37169i	0.707624	+	0.381750i
$199$	−13.6644			−0.968645			−0.484323	−	0.874889i	$-0.660934\pi$
$199$	−13.6644			−0.968645			−0.484323	+	0.874889i	$0.660934\pi$
$200$	−11.2713	+	0.978577i	−0.797002	+	0.0691959i
$201$	1.21377			0.0856127
$202$	22.3503	+	12.0575i	1.57256	+	0.848365i
$203$			0.643000i			0.0451298i
$204$	−0.244644	+	0.160750i	−0.0171285	+	0.0112548i
$205$			6.39312i			0.446515i
$206$	6.88240	−	12.7575i	0.479520	−	0.888854i
$207$	−19.9143			−1.38414
$208$	−3.67146	−	1.58757i	−0.254570	−	0.110078i
$209$	−10.7434			−0.743135
$210$	0.0143846	−	0.0266638i	0.000992633	−	0.00183998i
$211$			1.46052i			0.100546i	0.998736	+	0.0502731i	$0.0160092\pi$
$211$			1.46052i			0.100546i	−0.998736	+	0.0502731i	$0.983991\pi$
$212$	−15.0073	+	9.86098i	−1.03071	+	0.677255i
$213$		−	0.807653i		−	0.0553395i
$214$	−18.2787	−	9.86098i	−1.24950	−	0.674083i
$215$	−6.83221			−0.465953
$216$	0.214078	+	2.46576i	0.0145661	+	0.167774i
$217$	−0.192347			−0.0130573
$218$	18.3769	+	9.91400i	1.24464	+	0.671461i
$219$			1.02142i			0.0690214i
$220$	−2.94981	−	4.48929i	−0.198876	−	0.302668i
$221$			1.00000i			0.0672673i
$222$	0.391010	−	0.724789i	0.0262429	−	0.0486447i
$223$	7.12494			0.477121			0.238561	−	0.971128i	$-0.423324\pi$
$223$	7.12494			0.477121			0.238561	+	0.971128i	$0.423324\pi$
$224$	−0.512817	−	0.650039i	−0.0342640	−	0.0434325i
$225$	11.9143			0.794287
$226$	2.65708	−	4.92525i	0.176746	−	0.327623i
$227$			24.9357i			1.65504i	0.561434	+	0.827521i	$0.310250\pi$
$227$			24.9357i			1.65504i	−0.561434	+	0.827521i	$0.689750\pi$
$228$	−0.643000	−	0.978577i	−0.0425837	−	0.0648079i
$229$			2.95715i			0.195414i	0.995215	+	0.0977071i	$0.0311508\pi$
$229$			2.95715i			0.195414i	−0.995215	+	0.0977071i	$0.968849\pi$
$230$	8.32150	+	4.48929i	0.548703	+	0.296015i
$231$	−0.0575385			−0.00378576
$232$	1.07475	+	12.3790i	0.0705608	+	0.812724i
$233$	−5.19235			−0.340162			−0.170081	−	0.985430i	$-0.554403\pi$
$233$	−5.19235			−0.340162			−0.170081	+	0.985430i	$0.554403\pi$
$234$	3.70727	+	2.00000i	0.242352	+	0.130744i
$235$			7.12494i			0.464780i
$236$	−20.6430	+	13.5640i	−1.34374	+	0.882944i
$237$		−	2.20077i		−	0.142955i
$238$	−0.0982788	+	0.182173i	−0.00637047	+	0.0118085i
$239$	−14.3963			−0.931216			−0.465608	−	0.884991i	$-0.654164\pi$
$239$	−14.3963			−0.931216			−0.465608	+	0.884991i	$0.654164\pi$
$240$	0.232365	−	0.537375i	0.0149991	−	0.0346874i
$241$	23.3288			1.50274			0.751372	−	0.659879i	$-0.229393\pi$
$241$	23.3288			1.50274			0.751372	+	0.659879i	$0.229393\pi$
$242$	2.54231	−	4.71251i	0.163426	−	0.302932i
$243$		−	3.91431i		−	0.251103i
$244$	13.9572	−	9.17092i	0.893515	−	0.587108i
$245$			6.97858i			0.445845i
$246$	1.16465	+	0.628308i	0.0742555	+	0.0400594i
$247$	−4.00000			−0.254514
$248$	−3.70306	+	0.321500i	−0.235144	+	0.0204153i
$249$	0.628308			0.0398174
$250$	−11.2018	−	6.04315i	−0.708464	−	0.382203i
$251$		−	15.2713i		−	0.963916i	−0.876194	−	0.481958i	$-0.839926\pi$
$251$		−	15.2713i		−	0.963916i	0.876194	−	0.481958i	$-0.160074\pi$
$252$	0.478807	+	0.728692i	0.0301620	+	0.0459033i
$253$		−	17.9572i		−	1.12896i
$254$	−4.09617	+	7.59281i	−0.257017	+	0.476415i
$255$	−0.146365			−0.00916576
$256$	−10.9593	−	11.6574i	−0.684954	−	0.728587i
$257$	20.9143			1.30460			0.652299	−	0.757961i	$-0.273805\pi$
$257$	20.9143			1.30460			0.652299	+	0.757961i	$0.273805\pi$
$258$	−0.671462	+	1.24464i	−0.0418034	+	0.0774882i
$259$		−	0.582326i		−	0.0361840i
$260$	−1.09828	−	1.67146i	−0.0681124	−	0.103660i
$261$		−	13.0852i		−	0.809956i
$262$	18.4608	+	9.95926i	1.14051	+	0.615285i
$263$	13.0214			0.802935			0.401468	−	0.915873i	$-0.368500\pi$
$263$	13.0214			0.802935			0.401468	+	0.915873i	$0.368500\pi$
$264$	−1.10773	+	0.0961734i	−0.0681761	+	0.00591906i
$265$	−8.97858			−0.551550
$266$	−0.728692	−	0.393115i	−0.0446790	−	0.0241034i
$267$			0.786230i			0.0481165i
$268$	13.8610	−	9.10773i	0.846694	−	0.556343i
$269$			24.3503i			1.48466i	0.670033	+	0.742331i	$0.266280\pi$
$269$			24.3503i			1.48466i	−0.670033	+	0.742331i	$0.733720\pi$
$270$	−0.587567	+	1.08914i	−0.0357582	+	0.0662827i
$271$	25.5756			1.55361			0.776803	−	0.629743i	$-0.216840\pi$
$271$	25.5756			1.55361			0.776803	+	0.629743i	$0.216840\pi$
$272$	−1.58757	+	3.67146i	−0.0962604	+	0.222615i
$273$	−0.0214229			−0.00129657
$274$	6.55669	−	12.1537i	0.396104	−	0.734233i
$275$			10.7434i			0.647850i
$276$	1.63565	−	1.07475i	0.0984548	−	0.0646924i
$277$			4.43596i			0.266531i	0.991080	+	0.133266i	$0.0425463\pi$
$277$			4.43596i			0.266531i	−0.991080	+	0.133266i	$0.957454\pi$
$278$	−24.2397	−	13.0769i	−1.45380	−	0.784298i
$279$	3.91431			0.234344
$280$	−0.0358075	−	0.412433i	−0.00213991	−	0.0246476i
$281$	11.4145			0.680934			0.340467	−	0.940256i	$-0.389415\pi$
$281$	11.4145			0.680934			0.340467	+	0.940256i	$0.389415\pi$
$282$	1.29797	+	0.700231i	0.0772931	+	0.0416981i
$283$		−	19.4721i		−	1.15749i	−0.815507	−	0.578747i	$-0.803542\pi$
$283$		−	19.4721i		−	1.15749i	0.815507	−	0.578747i	$-0.196458\pi$
$284$	−6.06037	−	9.22322i	−0.359617	−	0.547298i
$285$		−	0.585462i		−	0.0346798i
$286$	−1.80344	+	3.34292i	−0.106640	+	0.197671i
$287$	0.935731			0.0552345
$288$	10.4360	+	13.2285i	0.614945	+	0.779495i
$289$	−16.0000			−0.941176
$290$	−2.94981	+	5.46787i	−0.173219	+	0.321084i
$291$			1.51492i			0.0888063i
$292$	7.66442	+	11.6644i	0.448526	+	0.682609i
$293$			10.8077i			0.631390i	0.948861	+	0.315695i	$0.102238\pi$
$293$			10.8077i			0.631390i	−0.948861	+	0.315695i	$0.897762\pi$
$294$	1.27131	+	0.685846i	0.0741442	+	0.0399994i
$295$	−12.3503			−0.719060
$296$	−0.973336	−	11.2109i	−0.0565740	−	0.651623i
$297$	2.35027			0.136376
$298$	−14.8824	−	8.02877i	−0.862115	−	0.465094i
$299$		−	6.68585i		−	0.386652i
$300$	−0.978577	+	0.643000i	−0.0564982	+	0.0371236i
$301$			1.00000i			0.0576390i
$302$	8.58757	−	15.9182i	0.494159	−	0.915990i
$303$	2.62831			0.150992
$304$	−14.6858	−	6.35027i	−0.842291	−	0.364213i
$305$	8.35027			0.478135
$306$	2.00000	−	3.70727i	0.114332	−	0.211930i
$307$			4.93573i			0.281697i	0.990031	+	0.140849i	$0.0449831\pi$
$307$			4.93573i			0.281697i	−0.990031	+	0.140849i	$0.955017\pi$
$308$	−0.657077	+	0.431750i	−0.0374404	+	0.0246012i
$309$		−	1.50023i		−	0.0853451i
$310$	−1.63565	−	0.882404i	−0.0928989	−	0.0501172i
$311$	0.786230			0.0445830			0.0222915	−	0.999752i	$-0.492904\pi$
$311$	0.786230			0.0445830			0.0222915	+	0.999752i	$0.492904\pi$
$312$	−0.412433	+	0.0358075i	−0.0233494	+	0.00202720i
$313$	−13.9357			−0.787694			−0.393847	−	0.919176i	$-0.628856\pi$
$313$	−13.9357			−0.787694			−0.393847	+	0.919176i	$0.628856\pi$
$314$	−27.0361	−	14.5855i	−1.52574	−	0.823105i
$315$			0.435961i			0.0245636i
$316$	−16.5138	−	25.1323i	−0.928976	−	1.41380i
$317$		−	19.9572i		−	1.12091i	−0.828186	−	0.560453i	$-0.810627\pi$
$317$		−	19.9572i		−	1.12091i	0.828186	−	0.560453i	$-0.189373\pi$
$318$	−0.882404	+	1.63565i	−0.0494827	+	0.0917229i
$319$	11.7992			0.660630
$320$	−1.37873	−	7.88030i	−0.0770734	−	0.440522i
$321$	−2.14950			−0.119973
$322$	0.657077	−	1.21798i	0.0366175	−	0.0678754i
$323$			4.00000i			0.222566i
$324$	−9.67326	−	14.7217i	−0.537403	−	0.817870i
$325$			4.00000i			0.221880i
$326$	−25.6932	−	13.8610i	−1.42301	−	0.767689i
$327$	2.16106			0.119507
$328$	18.0147	−	1.56404i	0.994695	−	0.0863596i
$329$	1.04285			0.0574939
$330$	−0.489289	−	0.263962i	−0.0269344	−	0.0145306i
$331$			11.7073i			0.643490i	0.946826	+	0.321745i	$0.104269\pi$
$331$			11.7073i			0.643490i	−0.946826	+	0.321745i	$0.895731\pi$
$332$	7.17513	−	4.71462i	0.393787	−	0.258748i
$333$			11.8505i			0.649403i
$334$	−12.0962	+	22.4219i	−0.661873	+	1.22687i
$335$	8.29273			0.453080
$336$	−0.0786532	−	0.0340102i	−0.00429088	−	0.00185541i
$337$	−0.807653			−0.0439957			−0.0219978	−	0.999758i	$-0.507003\pi$
$337$	−0.807653			−0.0439957			−0.0219978	+	0.999758i	$0.507003\pi$
$338$	−0.671462	+	1.24464i	−0.0365227	+	0.0676997i
$339$		−	0.579191i		−	0.0314573i
$340$	−1.67146	+	1.09828i	−0.0906477	+	0.0595625i
$341$			3.52962i			0.191139i
$342$	14.8291	+	8.00000i	0.801865	+	0.432590i
$343$	2.04598			0.110473
$344$	1.67146	+	19.2520i	0.0901192	+	1.03800i
$345$	0.978577			0.0526848
$346$	8.19656	+	4.42188i	0.440650	+	0.237722i
$347$			2.59702i			0.139415i	0.997567	+	0.0697076i	$0.0222066\pi$
$347$			2.59702i			0.139415i	−0.997567	+	0.0697076i	$0.977793\pi$
$348$	0.706194	+	1.07475i	0.0378560	+	0.0576127i
$349$		−	16.1709i		−	0.865610i	−0.901488	−	0.432805i	$-0.857524\pi$
$349$		−	16.1709i		−	0.865610i	0.901488	−	0.432805i	$-0.142476\pi$
$350$	−0.393115	+	0.728692i	−0.0210129	+	0.0389502i
$351$	0.875057			0.0467071
$352$	−11.9284	+	9.41033i	−0.635785	+	0.501572i
$353$	−5.32885			−0.283626			−0.141813	−	0.989893i	$-0.545293\pi$
$353$	−5.32885			−0.283626			−0.141813	+	0.989893i	$0.545293\pi$
$354$	−1.21377	+	2.24989i	−0.0645111	+	0.119580i
$355$		−	5.51806i		−	0.292868i
$356$	5.89962	+	8.97858i	0.312679	+	0.475864i
$357$			0.0214229i			0.00113382i
$358$	9.41064	+	5.07686i	0.497368	+	0.268320i
$359$	34.6002			1.82613			0.913063	−	0.407818i	$-0.133710\pi$
$359$	34.6002			1.82613			0.913063	+	0.407818i	$0.133710\pi$
$360$	0.728692	+	8.39312i	0.0384054	+	0.442356i
$361$	3.00000			0.157895
$362$	−0.782020	−	0.421884i	−0.0411020	−	0.0221738i
$363$		−	0.554173i		−	0.0290866i
$364$	−0.244644	+	0.160750i	−0.0128228	+	0.00842560i
$365$			6.97858i			0.365275i
$366$	0.820654	−	1.52119i	0.0428963	−	0.0795141i
$367$	−14.2499			−0.743838			−0.371919	−	0.928265i	$-0.621300\pi$
$367$	−14.2499			−0.743838			−0.371919	+	0.928265i	$0.621300\pi$
$368$	10.6142	−	24.5468i	0.553305	−	1.27959i
$369$	−19.0424			−0.991307
$370$	2.67146	−	4.95191i	0.138883	−	0.257438i
$371$			1.31415i			0.0682275i
$372$	−0.321500	+	0.211250i	−0.0166690	+	0.0109528i
$373$			15.1281i			0.783302i	0.920114	+	0.391651i	$0.128096\pi$
$373$			15.1281i			0.783302i	−0.920114	+	0.391651i	$0.871904\pi$
$374$	3.34292	+	1.80344i	0.172858	+	0.0932538i
$375$	−1.31729			−0.0680245
$376$	20.0769	−	1.74308i	1.03538	−	0.0898923i
$377$	4.39312			0.226257
$378$	0.159412	+	0.0859996i	0.00819926	+	0.00442334i
$379$		−	5.22846i		−	0.268568i	−0.990943	−	0.134284i	$-0.957127\pi$
$379$		−	5.22846i		−	0.268568i	0.990943	−	0.134284i	$-0.0428735\pi$
$380$	−4.39312	−	6.68585i	−0.225362	−	0.342977i
$381$			0.892886i			0.0457439i
$382$	−6.78202	+	12.5714i	−0.346998	+	0.643208i
$383$	27.3257			1.39628			0.698139	−	0.715962i	$-0.254012\pi$
$383$	27.3257			1.39628			0.698139	+	0.715962i	$0.254012\pi$
$384$	−1.57108	−	0.523299i	−0.0801737	−	0.0267045i
$385$	−0.393115			−0.0200350
$386$	−2.26396	+	4.19656i	−0.115233	+	0.213599i
$387$		−	20.3503i		−	1.03446i
$388$	11.3675	+	17.3001i	0.577096	+	0.878278i
$389$			9.02142i			0.457404i	0.973496	+	0.228702i	$0.0734482\pi$
$389$			9.02142i			0.457404i	−0.973496	+	0.228702i	$0.926552\pi$
$390$	−0.182173	−	0.0982788i	−0.00922469	−	0.00497654i
$391$	−6.68585			−0.338118
$392$	19.6644	−	1.70727i	0.993203	−	0.0862301i
$393$	2.17092			0.109509
$394$	−18.3236	−	9.88523i	−0.923130	−	0.498011i
$395$		−	15.0361i		−	0.756549i
$396$	13.3717	−	8.78623i	0.671953	−	0.441525i
$397$			35.0852i			1.76088i	0.474160	+	0.880439i	$0.342752\pi$
$397$			35.0852i			1.76088i	−0.474160	+	0.880439i	$0.657248\pi$
$398$	−9.17513	+	17.0073i	−0.459908	+	0.852501i
$399$	−0.0856914			−0.00428994
$400$	−6.35027	+	14.6858i	−0.317513	+	0.734292i
$401$	−1.06427			−0.0531470			−0.0265735	−	0.999647i	$-0.508460\pi$
$401$	−1.06427			−0.0531470			−0.0265735	+	0.999647i	$0.508460\pi$
$402$	0.815000	−	1.51071i	0.0406485	−	0.0753474i
$403$			1.31415i			0.0654627i
$404$	30.0147	−	19.7220i	1.49329	−	0.981204i
$405$		−	8.80765i		−	0.437656i
$406$	0.800307	+	0.431750i	0.0397186	+	0.0214274i
$407$	−10.6858			−0.529678
$408$	0.0358075	+	0.412433i	0.00177273	+	0.0204185i
$409$	−31.7220			−1.56855			−0.784275	−	0.620413i	$-0.786965\pi$
$409$	−31.7220			−1.56855			−0.784275	+	0.620413i	$0.786965\pi$
$410$	7.95715	+	4.29273i	0.392976	+	0.212003i
$411$		−	1.42923i		−	0.0704988i
$412$	−11.2572	−	17.1323i	−0.554604	−	0.844047i
$413$			1.80765i			0.0889488i
$414$	−13.3717	+	24.7862i	−0.657183	+	1.21818i
$415$	4.29273			0.210722
$416$	−4.44120	+	3.50367i	−0.217748	+	0.171782i
$417$	−2.85050			−0.139590
$418$	−7.21377	+	13.3717i	−0.352837	+	0.654031i
$419$			3.06740i			0.149852i	0.997189	+	0.0749262i	$0.0238721\pi$
$419$			3.06740i			0.149852i	−0.997189	+	0.0749262i	$0.976128\pi$
$420$	−0.0235283	−	0.0358075i	−0.00114806	−	0.00174723i
$421$			2.21377i			0.107893i	0.998544	+	0.0539463i	$0.0171800\pi$
$421$			2.21377i			0.107893i	−0.998544	+	0.0539463i	$0.982820\pi$
$422$	1.81783	+	0.980683i	0.0884904	+	0.0477389i
$423$	−21.2222			−1.03186
$424$	2.19656	+	25.3001i	0.106674	+	1.22868i
$425$	4.00000			0.194029
$426$	−1.00524	−	0.542308i	−0.0487041	−	0.0262749i
$427$		−	1.22219i		−	0.0591460i
$428$	−24.5468	+	16.1292i	−1.18652	+	0.779632i
$429$			0.393115i			0.0189798i
$430$	−4.58757	+	8.50367i	−0.221232	+	0.410084i
$431$	18.8898			0.909887			0.454944	−	0.890520i	$-0.349659\pi$
$431$	18.8898			0.909887			0.454944	+	0.890520i	$0.349659\pi$
$432$	3.21274	+	1.38921i	0.154573	+	0.0668385i
$433$	−21.8929			−1.05210			−0.526052	−	0.850452i	$-0.676328\pi$
$433$	−21.8929			−1.05210			−0.526052	+	0.850452i	$0.676328\pi$
$434$	−0.129153	+	0.239403i	−0.00619956	+	0.0114917i
$435$			0.643000i			0.0308295i
$436$	24.6788	−	16.2159i	1.18190	−	0.776600i
$437$		−	26.7434i		−	1.27931i
$438$	1.27131	+	0.685846i	0.0607455	+	0.0327710i
$439$	13.8077			0.659003			0.329502	−	0.944155i	$-0.393119\pi$
$439$	13.8077			0.659003			0.329502	+	0.944155i	$0.393119\pi$
$440$	−7.56825	+	0.657077i	−0.360802	+	0.0313249i
$441$	−20.7862			−0.989820
$442$	1.24464	+	0.671462i	0.0592017	+	0.0319382i
$443$			25.5756i			1.21513i	0.794269	+	0.607567i	$0.207854\pi$
$443$			25.5756i			1.21513i	−0.794269	+	0.607567i	$0.792146\pi$
$444$	−0.639557	−	0.973336i	−0.0303520	−	0.0461925i
$445$			5.37169i			0.254643i
$446$	4.78412	−	8.86802i	0.226535	−	0.419913i
$447$	−1.75011			−0.0827776
$448$	−1.15340	+	0.201799i	−0.0544932	+	0.00953409i
$449$	−24.3074			−1.14714			−0.573569	−	0.819157i	$-0.694442\pi$
$449$	−24.3074			−1.14714			−0.573569	+	0.819157i	$0.694442\pi$
$450$	8.00000	−	14.8291i	0.377124	−	0.699049i
$451$		−	17.1709i		−	0.808547i
$452$	−4.34606	−	6.61423i	−0.204421	−	0.311107i
$453$		−	1.87192i		−	0.0879506i
$454$	31.0361	+	16.7434i	1.45660	+	0.785806i
$455$	−0.146365			−0.00686172
$456$	−1.64973	+	0.143230i	−0.0772557	+	0.00670736i
$457$	12.2008			0.570728			0.285364	−	0.958419i	$-0.407886\pi$
$457$	12.2008			0.570728			0.285364	+	0.958419i	$0.407886\pi$
$458$	3.68061	+	1.98562i	0.171983	+	0.0927817i
$459$		−	0.875057i		−	0.0408442i
$460$	11.1751	−	7.34292i	0.521043	−	0.342366i
$461$			8.02142i			0.373595i	0.982398	+	0.186797i	$0.0598108\pi$
$461$			8.02142i			0.373595i	−0.982398	+	0.186797i	$0.940189\pi$
$462$	−0.0386349	+	0.0716150i	−0.00179746	+	0.00333183i
$463$	−36.0575			−1.67574			−0.837868	−	0.545873i	$-0.816198\pi$
$463$	−36.0575			−1.67574			−0.837868	+	0.545873i	$0.816198\pi$
$464$	16.1292	+	6.97437i	0.748777	+	0.323777i
$465$	−0.192347			−0.00891987
$466$	−3.48646	+	6.46262i	−0.161507	+	0.299375i
$467$		−	19.1856i		−	0.887804i	−0.896075	−	0.443902i	$-0.853594\pi$
$467$		−	19.1856i		−	0.887804i	0.896075	−	0.443902i	$-0.146406\pi$
$468$	4.97858	−	3.27131i	0.230135	−	0.151216i
$469$		−	1.21377i		−	0.0560467i
$470$	8.86802	+	4.78412i	0.409051	+	0.220675i
$471$	−3.17935			−0.146497
$472$	3.02142	+	34.8009i	0.139072	+	1.60184i
$473$	18.3503			0.843746
$474$	−2.73917	−	1.47773i	−0.125814	−	0.0678744i
$475$			16.0000i			0.734130i
$476$	0.160750	+	0.244644i	0.00736797	+	0.0112133i
$477$		−	26.7434i		−	1.22450i
$478$	−9.66653	+	17.9182i	−0.442137	+	0.819560i
$479$	−11.9112			−0.544235			−0.272118	−	0.962264i	$-0.587724\pi$
$479$	−11.9112			−0.544235			−0.272118	+	0.962264i	$0.587724\pi$
$480$	−0.512817	−	0.650039i	−0.0234068	−	0.0296701i
$481$	−3.97858			−0.181408
$482$	15.6644	−	29.0361i	0.713495	−	1.32256i
$483$		−	0.143230i		−	0.00651719i
$484$	−4.15834	−	6.32854i	−0.189015	−	0.287661i
$485$			10.3503i			0.469982i
$486$	−4.87192	−	2.62831i	−0.220995	−	0.119222i
$487$	−15.8568			−0.718539			−0.359269	−	0.933234i	$-0.616974\pi$
$487$	−15.8568			−0.718539			−0.359269	+	0.933234i	$0.616974\pi$
$488$	−2.04285	−	23.5296i	−0.0924753	−	1.06514i
$489$	−3.02142			−0.136633
$490$	8.68585	+	4.68585i	0.392387	+	0.211685i
$491$			3.91117i			0.176509i	0.996098	+	0.0882544i	$0.0281288\pi$
$491$			3.91117i			0.176509i	−0.996098	+	0.0882544i	$0.971871\pi$
$492$	1.56404	−	1.02769i	0.0705123	−	0.0463320i
$493$		−	4.39312i		−	0.197856i
$494$	−2.68585	+	4.97858i	−0.120842	+	0.223997i
$495$	8.00000			0.359573
$496$	−2.08631	+	4.82487i	−0.0936780	+	0.216643i
$497$	−0.807653			−0.0362282
$498$	0.421884	−	0.782020i	0.0189051	−	0.0350431i
$499$		−	23.1793i		−	1.03765i	−0.854880	−	0.518825i	$-0.826370\pi$
$499$		−	23.1793i		−	1.03765i	0.854880	−	0.518825i	$-0.173630\pi$
$500$	−15.0432	+	9.88451i	−0.672750	+	0.442049i
$501$			2.63673i			0.117800i
$502$	−19.0073	−	10.2541i	−0.848339	−	0.457663i
$503$	18.5426			0.826774			0.413387	−	0.910555i	$-0.364346\pi$
$503$	18.5426			0.826774			0.413387	+	0.910555i	$0.364346\pi$
$504$	1.22846	−	0.106655i	0.0547201	−	0.00475081i
$505$	17.9572			0.799083
$506$	−22.3503	−	12.0575i	−0.993591	−	0.536023i
$507$			0.146365i			0.00650032i
$508$	6.69992	+	10.1966i	0.297261	+	0.452399i
$509$		−	25.9143i		−	1.14863i	−0.818634	−	0.574316i	$-0.805268\pi$
$509$		−	25.9143i		−	1.14863i	0.818634	−	0.574316i	$-0.194732\pi$
$510$	−0.0982788	+	0.182173i	−0.00435186	+	0.00806675i
$511$	1.02142			0.0451851
$512$	−21.8680	+	5.81289i	−0.966439	+	0.256896i
$513$	3.50023			0.154539
$514$	14.0432	−	26.0309i	0.619417	−	1.14817i
$515$		−	10.2499i		−	0.451664i
$516$	1.09828	+	1.67146i	0.0483490	+	0.0735820i
$517$		−	19.1365i		−	0.841622i
$518$	−0.724789	−	0.391010i	−0.0318454	−	0.0171800i
$519$	0.963884			0.0423098
$520$	−2.81783	+	0.244644i	−0.123570	+	0.0107284i
$521$	−12.7648			−0.559236			−0.279618	−	0.960111i	$-0.590208\pi$
$521$	−12.7648			−0.559236			−0.279618	+	0.960111i	$0.590208\pi$
$522$	−16.2865	−	8.78623i	−0.712839	−	0.384563i
$523$			27.1856i			1.18874i	0.804190	+	0.594372i	$0.202599\pi$
$523$			27.1856i			1.18874i	−0.804190	+	0.594372i	$0.797401\pi$
$524$	24.7915	−	16.2899i	1.08302	−	0.711628i
$525$			0.0856914i			0.00373988i
$526$	8.74338	−	16.2070i	0.381230	−	0.706661i
$527$	1.31415			0.0572454
$528$	−0.624097	+	1.44331i	−0.0271603	+	0.0628119i
$529$	21.7005			0.943502
$530$	−6.02877	+	11.1751i	−0.261873	+	0.485417i
$531$		−	36.7862i		−	1.59639i
$532$	−0.978577	+	0.643000i	−0.0424267	+	0.0278776i
$533$		−	6.39312i		−	0.276917i
$534$	0.978577	+	0.527923i	0.0423472	+	0.0228455i
$535$	−14.6858			−0.634924
$536$	−2.02877	−	23.3675i	−0.0876295	−	1.00932i
$537$	1.10666			0.0477557
$538$	30.3074	+	16.3503i	1.30665	+	0.704910i
$539$		−	18.7434i		−	0.807335i
$540$	0.961057	+	1.46262i	0.0413573	+	0.0629413i
$541$		−	6.76481i		−	0.290842i	−0.989370	−	0.145421i	$-0.953546\pi$
$541$		−	6.76481i		−	0.290842i	0.989370	−	0.145421i	$-0.0464536\pi$
$542$	17.1730	−	31.8325i	0.737645	−	1.36732i
$543$	−0.0919626			−0.00394649
$544$	3.50367	+	4.44120i	0.150219	+	0.190415i
$545$	14.7648			0.632455
$546$	−0.0143846	+	0.0266638i	−0.000615605	+	0.00114111i
$547$			15.3832i			0.657740i	0.944375	+	0.328870i	$0.106668\pi$
$547$			15.3832i			0.657740i	−0.944375	+	0.328870i	$0.893332\pi$
$548$	−10.7245	−	16.3215i	−0.458127	−	0.697220i
$549$			24.8719i			1.06151i
$550$	13.3717	+	7.21377i	0.570171	+	0.307596i
$551$	17.5725			0.748612
$552$	−0.239403	−	2.75746i	−0.0101897	−	0.117365i
$553$	−2.20077			−0.0935862
$554$	5.52119	+	2.97858i	0.234573	+	0.126548i
$555$		−	0.582326i		−	0.0247184i
$556$	−32.5521	+	21.3892i	−1.38052	+	0.907105i
$557$			7.59388i			0.321763i	0.986974	+	0.160882i	$0.0514337\pi$
$557$			7.59388i			0.321763i	−0.986974	+	0.160882i	$0.948566\pi$
$558$	2.62831	−	4.87192i	0.111265	−	0.206245i
$559$	6.83221			0.288972
$560$	−0.537375	−	0.232365i	−0.0227082	−	0.00981922i
$561$	0.393115			0.0165973
$562$	7.66442	−	14.2070i	0.323304	−	0.599288i
$563$			14.9754i			0.631140i	0.948902	+	0.315570i	$0.102196\pi$
$563$			14.9754i			0.631140i	−0.948902	+	0.315570i	$0.897804\pi$
$564$	1.74308	−	1.14534i	0.0733968	−	0.0482273i
$565$		−	3.95715i		−	0.166479i
$566$	−24.2358	−	13.0748i	−1.01871	−	0.549573i
$567$	−1.28914			−0.0541386
$568$	−15.5489	+	1.34996i	−0.652419	+	0.0566431i
$569$	−4.25662			−0.178447			−0.0892233	−	0.996012i	$-0.528438\pi$
$569$	−4.25662			−0.178447			−0.0892233	+	0.996012i	$0.528438\pi$
$570$	−0.728692	−	0.393115i	−0.0305215	−	0.0164658i
$571$			43.5903i			1.82420i	0.409971	+	0.912098i	$0.365539\pi$
$571$			43.5903i			1.82420i	−0.409971	+	0.912098i	$0.634461\pi$
$572$	2.94981	+	4.48929i	0.123338	+	0.187707i
$573$			1.47835i			0.0617589i
$574$	0.628308	−	1.16465i	0.0262251	−	0.0486117i
$575$	−26.7434			−1.11528
$576$	23.4721	−	4.10666i	0.978003	−	0.171111i
$577$	43.5934			1.81482			0.907409	−	0.420249i	$-0.138057\pi$
$577$	43.5934			1.81482			0.907409	+	0.420249i	$0.138057\pi$
$578$	−10.7434	+	19.9143i	−0.446866	+	0.828326i
$579$			0.493499i			0.0205091i
$580$	4.82487	+	7.34292i	0.200342	+	0.304898i
$581$		−	0.628308i		−	0.0260666i
$582$	1.88554	+	1.01721i	0.0781581	+	0.0421648i
$583$	24.1151			0.998744
$584$	19.6644	−	1.70727i	0.813720	−	0.0706473i
$585$	2.97858			0.123149
$586$	13.4517	+	7.25692i	0.555684	+	0.299781i
$587$			1.31415i			0.0542409i	0.999632	+	0.0271205i	$0.00863377\pi$
$587$			1.31415i			0.0542409i	−0.999632	+	0.0271205i	$0.991366\pi$
$588$	1.70727	−	1.12181i	0.0704066	−	0.0462625i
$589$			5.25662i			0.216595i
$590$	−8.29273	+	15.3717i	−0.341406	+	0.632843i
$591$	−2.15479			−0.0886361
$592$	−14.6072	−	6.31626i	−0.600352	−	0.259597i
$593$	−0.777809			−0.0319408			−0.0159704	−	0.999872i	$-0.505084\pi$
$593$	−0.777809			−0.0319408			−0.0159704	+	0.999872i	$0.505084\pi$
$594$	1.57812	−	2.92525i	0.0647509	−	0.120024i
$595$			0.146365i			0.00600040i
$596$	−19.9859	+	13.1323i	−0.818655	+	0.537920i
$597$			2.00000i			0.0818546i
$598$	−8.32150	−	4.48929i	−0.340291	−	0.183581i
$599$	3.36327			0.137420			0.0687098	−	0.997637i	$-0.478112\pi$
$599$	3.36327			0.137420			0.0687098	+	0.997637i	$0.478112\pi$
$600$	0.143230	+	1.64973i	0.00584734	+	0.0673500i
$601$	4.17092			0.170136			0.0850678	−	0.996375i	$-0.472889\pi$
$601$	4.17092			0.170136			0.0850678	+	0.996375i	$0.472889\pi$
$602$	1.24464	+	0.671462i	0.0507279	+	0.0273667i
$603$			24.7005i			1.00588i
$604$	−14.0463	−	21.3769i	−0.571535	−	0.869815i
$605$		−	3.78623i		−	0.153932i
$606$	1.76481	−	3.27131i	0.0716904	−	0.132888i
$607$	−34.8929			−1.41626			−0.708129	−	0.706083i	$-0.750461\pi$
$607$	−34.8929			−1.41626			−0.708129	+	0.706083i	$0.750461\pi$
$608$	−17.7648	+	14.0147i	−0.720458	+	0.568371i
$609$	0.0941131			0.00381365
$610$	5.60688	−	10.3931i	0.227016	−	0.420805i
$611$		−	7.12494i		−	0.288244i
$612$	−3.27131	−	4.97858i	−0.132235	−	0.201247i
$613$			17.9143i			0.723552i	0.932265	+	0.361776i	$0.117829\pi$
$613$			17.9143i			0.723552i	−0.932265	+	0.361776i	$0.882171\pi$
$614$	6.14323	+	3.31415i	0.247921	+	0.133748i
$615$	0.935731			0.0377323
$616$	0.0961734	+	1.10773i	0.00387494	+	0.0446317i
$617$	23.9143			0.962754			0.481377	−	0.876514i	$-0.340137\pi$
$617$	23.9143			0.962754			0.481377	+	0.876514i	$0.340137\pi$
$618$	−1.86725	−	1.00735i	−0.0751119	−	0.0405214i
$619$			27.9656i			1.12403i	0.827127	+	0.562016i	$0.189974\pi$
$619$			27.9656i			1.12403i	−0.827127	+	0.562016i	$0.810026\pi$
$620$	−2.19656	+	1.44331i	−0.0882159	+	0.0579646i
$621$			5.85050i			0.234772i
$622$	0.527923	−	0.978577i	0.0211678	−	0.0392374i
$623$	0.786230			0.0314997
$624$	−0.232365	+	0.537375i	−0.00930205	+	0.0215122i
$625$	11.0000			0.440000
$626$	−9.35731	+	17.3450i	−0.373993	+	0.693247i
$627$			1.57246i			0.0627980i
$628$	−36.3074	+	23.8568i	−1.44882	+	0.951989i
$629$			3.97858i			0.158636i
$630$	0.542616	+	0.292731i	0.0216183	+	0.0116627i
$631$	−28.4966			−1.13443			−0.567217	−	0.823569i	$-0.691980\pi$
$631$	−28.4966			−1.13443			−0.567217	+	0.823569i	$0.691980\pi$
$632$	−42.3692	+	3.67850i	−1.68536	+	0.146323i
$633$	0.213770			0.00849658
$634$	−24.8396	−	13.4005i	−0.986505	−	0.532200i
$635$			6.10038i			0.242086i
$636$	1.44331	+	2.19656i	0.0572309	+	0.0870992i
$637$		−	6.97858i		−	0.276501i
$638$	7.92273	−	14.6858i	0.313664	−	0.581418i
$639$	16.4360			0.650197
$640$	−10.7339	−	3.57529i	−0.424296	−	0.141326i
$641$	13.9143			0.549582			0.274791	−	0.961504i	$-0.411391\pi$
$641$	13.9143			0.549582			0.274791	+	0.961504i	$0.411391\pi$
$642$	−1.44331	+	2.67536i	−0.0569628	+	0.105588i
$643$		−	19.0361i		−	0.750711i	−0.926881	−	0.375356i	$-0.877521\pi$
$643$		−	19.0361i		−	0.750711i	0.926881	−	0.375356i	$-0.122479\pi$
$644$	−1.07475	−	1.63565i	−0.0423511	−	0.0644538i
$645$			1.00000i			0.0393750i
$646$	4.97858	+	2.68585i	0.195879	+	0.105673i
$647$	−17.6069			−0.692198			−0.346099	−	0.938198i	$-0.612494\pi$
$647$	−17.6069			−0.692198			−0.346099	+	0.938198i	$0.612494\pi$
$648$	−24.8184	+	2.15474i	−0.974961	+	0.0846463i
$649$	33.1709			1.30207
$650$	4.97858	+	2.68585i	0.195276	+	0.105348i
$651$			0.0281529i			0.00110340i
$652$	−34.5040	+	22.6718i	−1.35128	+	0.887895i
$653$			33.8715i			1.32549i	0.748844	+	0.662746i	$0.230609\pi$
$653$			33.8715i			1.32549i	−0.748844	+	0.662746i	$0.769391\pi$
$654$	1.45107	−	2.68975i	0.0567412	−	0.105178i
$655$	14.8322			0.579542
$656$	10.1495	−	23.4721i	0.396271	−	0.916431i
$657$	−20.7862			−0.810948
$658$	0.700231	−	1.29797i	0.0272978	−	0.0506002i
$659$			27.1856i			1.05900i	0.848310	+	0.529501i	$0.177621\pi$
$659$			27.1856i			1.05900i	−0.848310	+	0.529501i	$0.822379\pi$
$660$	−0.657077	+	0.431750i	−0.0255767	+	0.0168058i
$661$		−	48.2730i		−	1.87760i	−0.344460	−	0.938801i	$-0.611938\pi$
$661$		−	48.2730i		−	1.87760i	0.344460	−	0.938801i	$-0.388062\pi$
$662$	14.5714	+	7.86098i	0.566333	+	0.305526i
$663$	0.146365			0.00568436
$664$	−1.05019	−	12.0962i	−0.0407554	−	0.469423i
$665$	−0.585462			−0.0227032
$666$	14.7497	+	7.95715i	0.571538	+	0.308333i
$667$			29.3717i			1.13728i
$668$	19.7852	+	30.1109i	0.765511	+	1.16502i
$669$		−	1.04285i		−	0.0403187i
$670$	5.56825	−	10.3215i	0.215120	−	0.398754i
$671$	−22.4275			−0.865806
$672$	−0.0951432	+	0.0750587i	−0.00367023	+	0.00289545i
$673$	5.78623			0.223043			0.111521	−	0.993762i	$-0.464428\pi$
$673$	5.78623			0.223043			0.111521	+	0.993762i	$0.464428\pi$
$674$	−0.542308	+	1.00524i	−0.0208889	+	0.0387204i
$675$		−	3.50023i		−	0.134724i
$676$	1.09828	+	1.67146i	0.0422415	+	0.0642870i
$677$			37.3288i			1.43466i	0.696731	+	0.717332i	$0.254637\pi$
$677$			37.3288i			1.43466i	−0.696731	+	0.717332i	$0.745363\pi$
$678$	−0.720887	−	0.388904i	−0.0276855	−	0.0149358i
$679$	1.51492			0.0581374
$680$	0.244644	+	2.81783i	0.00938168	+	0.108059i
$681$	3.64973			0.139858
$682$	4.39312	+	2.37000i	0.168221	+	0.0907520i
$683$			17.6644i			0.675910i	0.941162	+	0.337955i	$0.109735\pi$
$683$			17.6644i			0.675910i	−0.941162	+	0.337955i	$0.890265\pi$
$684$	19.9143	−	13.0852i	0.761443	−	0.500326i
$685$		−	9.76481i		−	0.373094i
$686$	1.37380	−	2.54652i	0.0524518	−	0.0972265i
$687$	0.432825			0.0165133
$688$	25.0842	+	10.8466i	0.956326	+	0.413523i
$689$	8.97858			0.342057
$690$	0.657077	−	1.21798i	0.0250145	−	0.0463677i
$691$		−	44.4998i		−	1.69285i	−0.532507	−	0.846426i	$-0.678750\pi$
$691$		−	44.4998i		−	1.69285i	0.532507	−	0.846426i	$-0.321250\pi$
$692$	11.0073	−	7.23267i	0.418437	−	0.274945i
$693$		−	1.17092i		−	0.0444797i
$694$	3.23237	+	1.74380i	0.122699	+	0.0661937i
$695$	−19.4752			−0.738737
$696$	1.81186	−	0.157306i	0.0686785	−	0.00596268i
$697$	−6.39312			−0.242157
$698$	−20.1270	−	10.8582i	−0.761820	−	0.410987i
$699$			0.759980i			0.0287451i
$700$	0.643000	+	0.978577i	0.0243031	+	0.0369867i
$701$		−	17.0643i		−	0.644509i	−0.946653	−	0.322254i	$-0.895559\pi$
$701$		−	17.0643i		−	0.644509i	0.946653	−	0.322254i	$-0.104441\pi$
$702$	0.587567	−	1.08914i	0.0221763	−	0.0411068i
$703$	−15.9143			−0.600220
$704$	3.70306	+	21.1653i	0.139564	+	0.797696i
$705$	1.04285			0.0392758
$706$	−3.57812	+	6.63252i	−0.134664	+	0.249618i
$707$		−	2.62831i		−	0.0988477i
$708$	1.98531	+	3.02142i	0.0746124	+	0.113552i
$709$		−	0.427539i		−	0.0160566i	−0.999968	−	0.00802829i	$-0.997444\pi$
$709$		−	0.427539i		−	0.0160566i	0.999968	−	0.00802829i	$-0.00255551\pi$
$710$	−6.86802	−	3.70516i	−0.257752	−	0.139052i
$711$	44.7862			1.67961
$712$	15.1365	−	1.31415i	0.567264	−	0.0492500i
$713$	−8.78623			−0.329047
$714$	0.0266638	+	0.0143846i	0.000997869	+	0.000538331i
$715$			2.68585i			0.100445i
$716$	12.6378	−	8.30398i	0.472295	−	0.310334i
$717$			2.10711i			0.0786916i
$718$	23.2327	−	43.0649i	0.867036	−	1.60717i
$719$	37.3780			1.39396			0.696981	−	0.717089i	$-0.254526\pi$
$719$	37.3780			1.39396			0.696981	+	0.717089i	$0.254526\pi$
$720$	10.9357	+	4.72869i	0.407551	+	0.176228i
$721$	−1.50023			−0.0558715
$722$	2.01438	−	3.73393i	0.0749676	−	0.138963i
$723$		−	3.41454i		−	0.126988i
$724$	−1.05019	+	0.690057i	−0.0390301	+	0.0256458i
$725$		−	17.5725i		−	0.652625i
$726$	−0.689749	−	0.372106i	−0.0255990	−	0.0138102i
$727$	14.4851			0.537222			0.268611	−	0.963249i	$-0.413435\pi$
$727$	14.4851			0.537222			0.268611	+	0.963249i	$0.413435\pi$
$728$	0.0358075	+	0.412433i	0.00132711	+	0.0152858i
$729$	25.8500			0.957409
$730$	8.68585	+	4.68585i	0.321478	+	0.173431i
$731$		−	6.83221i		−	0.252698i
$732$	−1.34231	−	2.04285i	−0.0496131	−	0.0755058i
$733$		−	0.299461i		−	0.0110608i	−0.999985	−	0.00553042i	$-0.998240\pi$
$733$		−	0.299461i		−	0.0110608i	0.999985	−	0.00553042i	$-0.00176040\pi$
$734$	−9.56825	+	17.7360i	−0.353171	+	0.654649i
$735$	1.02142			0.0376757
$736$	−23.4250	−	29.6932i	−0.863458	−	1.09451i
$737$	−22.2730			−0.820436
$738$	−12.7862	+	23.7010i	−0.470668	+	0.872446i
$739$		−	18.9786i		−	0.698138i	−0.937097	−	0.349069i	$-0.886498\pi$
$739$		−	18.9786i		−	0.698138i	0.937097	−	0.349069i	$-0.113502\pi$
$740$	−4.36959	−	6.65004i	−0.160629	−	0.244460i
$741$			0.585462i			0.0215075i
$742$	1.63565	+	0.882404i	0.0600467	+	0.0323941i
$743$	−26.7465			−0.981235			−0.490617	−	0.871375i	$-0.663229\pi$
$743$	−26.7465			−0.981235			−0.490617	+	0.871375i	$0.663229\pi$
$744$	0.0470565	+	0.542000i	0.00172518	+	0.0198707i
$745$	−11.9572			−0.438076
$746$	18.8291	+	10.1579i	0.689381	+	0.371908i
$747$			12.7862i			0.467824i
$748$	4.48929	−	2.94981i	0.164145	−	0.107856i
$749$			2.14950i			0.0785411i
$750$	−0.884509	+	1.63956i	−0.0322977	+	0.0598681i
$751$	−14.1923			−0.517886			−0.258943	−	0.965893i	$-0.583374\pi$
$751$	−14.1923			−0.517886			−0.258943	+	0.965893i	$0.583374\pi$
$752$	11.3113	−	26.1590i	0.412482	−	0.953919i
$753$	−2.23519			−0.0814549
$754$	2.94981	−	5.46787i	0.107426	−	0.199128i
$755$		−	12.7894i		−	0.465453i
$756$	0.214078	−	0.140666i	0.00778593	−	0.00511596i
$757$		−	45.5934i		−	1.65712i	−0.559899	−	0.828561i	$-0.689160\pi$
$757$		−	45.5934i		−	1.65712i	0.559899	−	0.828561i	$-0.310840\pi$
$758$	−6.50758	−	3.51071i	−0.236366	−	0.127515i
$759$	−2.62831			−0.0954015
$760$	−11.2713	+	0.978577i	−0.408853	+	0.0354967i
$761$	−37.6363			−1.36431			−0.682157	−	0.731206i	$-0.738958\pi$
$761$	−37.6363			−1.36431			−0.682157	+	0.731206i	$0.738958\pi$
$762$	1.11133	+	0.599538i	0.0402591	+	0.0217190i
$763$		−	2.16106i		−	0.0782356i
$764$	11.0930	+	16.8824i	0.401332	+	0.610784i
$765$		−	2.97858i		−	0.107691i
$766$	18.3482	−	34.0108i	0.662946	−	1.22886i
$767$	12.3503			0.445942
$768$	−1.70624	+	1.60406i	−0.0615686	+	0.0578814i
$769$	0.700539			0.0252621			0.0126310	−	0.999920i	$-0.495979\pi$
$769$	0.700539			0.0252621			0.0126310	+	0.999920i	$0.495979\pi$
$770$	−0.263962	+	0.489289i	−0.00951252	+	0.0176327i
$771$		−	3.06113i		−	0.110244i
$772$	3.70306	+	5.63565i	0.133276	+	0.202832i
$773$		−	5.08569i		−	0.182920i	−0.995809	−	0.0914598i	$-0.970847\pi$
$773$		−	5.08569i		−	0.182920i	0.995809	−	0.0914598i	$-0.0291533\pi$
$774$	−25.3288	−	13.6644i	−0.910427	−	0.491158i
$775$	5.25662			0.188823
$776$	29.1653	−	2.53213i	1.04697	−	0.0908983i
$777$	−0.0852325			−0.00305770
$778$	11.2285	+	6.05754i	0.402560	+	0.217173i
$779$		−	25.5725i		−	0.916228i
$780$	−0.244644	+	0.160750i	−0.00875967	+	0.00575578i
$781$			14.8207i			0.530325i
$782$	−4.48929	+	8.32150i	−0.160537	+	0.297576i
$783$	−3.84423			−0.137381
$784$	11.0790	−	25.6216i	0.395677	−	0.915056i
$785$	−21.7220			−0.775290
$786$	1.45769	−	2.70203i	0.0519941	−	0.0963781i
$787$			14.3074i			0.510005i	0.966940	+	0.255002i	$0.0820762\pi$
$787$			14.3074i			0.510005i	−0.966940	+	0.255002i	$0.917924\pi$
$788$	−24.6072	+	16.1688i	−0.876595	+	0.575990i
$789$		−	1.90589i		−	0.0678514i
$790$	−18.7146	−	10.0962i	−0.665836	−	0.359206i
$791$	−0.579191			−0.0205937
$792$	−1.95715	−	22.5426i	−0.0695444	−	0.801017i
$793$	−8.35027			−0.296527
$794$	43.6686	+	23.5584i	1.54974	+	0.836056i
$795$			1.31415i			0.0466082i
$796$	15.0073	+	22.8396i	0.531921	+	0.809527i
$797$		−	2.54262i		−	0.0900641i	−0.998986	−	0.0450320i	$-0.985661\pi$
$797$		−	2.54262i		−	0.0900641i	0.998986	−	0.0450320i	$-0.0143390\pi$
$798$	−0.0575385	+	0.106655i	−0.00203684	+	0.00377556i
$799$	−7.12494			−0.252062
$800$	14.0147	+	17.7648i	0.495494	+	0.628081i
$801$	−16.0000			−0.565332
$802$	−0.714615	+	1.32464i	−0.0252339	+	0.0467745i
$803$		−	18.7434i		−	0.661440i
$804$	−1.33306	−	2.02877i	−0.0470133	−	0.0715492i
$805$		−	0.978577i		−	0.0344903i
$806$	1.63565	+	0.882404i	0.0576135	+	0.0310813i
$807$	3.56404			0.125460
$808$	−4.39312	−	50.6002i	−0.154549	−	1.78011i
$809$	−33.1495			−1.16547			−0.582737	−	0.812661i	$-0.698018\pi$
$809$	−33.1495			−1.16547			−0.582737	+	0.812661i	$0.698018\pi$
$810$	−10.9624	−	5.91400i	−0.385179	−	0.207797i
$811$		−	1.28600i		−	0.0451576i	−0.999745	−	0.0225788i	$-0.992812\pi$
$811$		−	1.28600i		−	0.0451576i	0.999745	−	0.0225788i	$-0.00718767\pi$
$812$	1.07475	−	0.706194i	0.0377163	−	0.0247825i
$813$		−	3.74338i		−	0.131286i
$814$	−7.17513	+	13.3001i	−0.251488	+	0.466167i
$815$	−20.6430			−0.723093
$816$	0.537375	+	0.232365i	0.0188119	+	0.00813440i
$817$	27.3288			0.956115
$818$	−21.3001	+	39.4826i	−0.744740	+	1.38048i
$819$		−	0.435961i		−	0.0152337i
$820$	10.6858	−	7.02142i	0.373166	−	0.245199i
$821$			11.7005i			0.408352i	0.978934	+	0.204176i	$0.0654514\pi$
$821$			11.7005i			0.408352i	−0.978934	+	0.204176i	$0.934549\pi$
$822$	−1.77888	−	0.959674i	−0.0620457	−	0.0334725i
$823$	−38.9786			−1.35871			−0.679354	−	0.733811i	$-0.737740\pi$
$823$	−38.9786			−1.35871			−0.679354	+	0.733811i	$0.737740\pi$
$824$	−28.8824	+	2.50758i	−1.00617	+	0.0873555i
$825$	1.57246			0.0547461
$826$	2.24989	+	1.21377i	0.0782835	+	0.0422324i
$827$		−	43.5296i		−	1.51367i	−0.653604	−	0.756837i	$-0.726744\pi$
$827$		−	43.5296i		−	1.51367i	0.653604	−	0.756837i	$-0.273256\pi$
$828$	21.8715	+	33.2860i	0.760086	+	1.15677i
$829$		−	35.0852i		−	1.21856i	−0.792955	−	0.609280i	$-0.791458\pi$
$829$		−	35.0852i		−	1.21856i	0.792955	−	0.609280i	$-0.208542\pi$
$830$	2.88240	−	5.34292i	0.100050	−	0.185456i
$831$	0.649272			0.0225230
$832$	1.37873	+	7.88030i	0.0477989	+	0.273200i
$833$	−6.97858			−0.241793
$834$	−1.91400	+	3.54786i	−0.0662764	+	0.122852i
$835$			18.0147i			0.623424i
$836$	11.7992	+	17.9572i	0.408085	+	0.621061i
$837$		−	1.14996i		−	0.0397484i
$838$	3.81783	+	2.05964i	0.131885	+	0.0711492i
$839$	−10.4851			−0.361985			−0.180993	−	0.983484i	$-0.557931\pi$
$839$	−10.4851			−0.361985			−0.180993	+	0.983484i	$0.557931\pi$
$840$	−0.0603659	+	0.00524098i	−0.00208282	+	0.000180831i
$841$	9.70054			0.334501
$842$	2.75536	+	1.48646i	0.0949558	+	0.0512268i
$843$		−	1.67069i		−	0.0575418i
$844$	2.44120	−	1.60406i	0.0840296	−	0.0552139i
$845$			1.00000i			0.0344010i
$846$	−14.2499	+	26.4141i	−0.489921	+	0.908135i
$847$	−0.554173			−0.0190416
$848$	32.9645	+	14.2541i	1.13201	+	0.489488i
$849$	−2.85004			−0.0978131
$850$	2.68585	−	4.97858i	0.0921238	−	0.170764i
$851$		−	26.6002i		−	0.911842i
$852$	−1.34996	+	0.887028i	−0.0462489	+	0.0303891i
$853$			40.5296i			1.38771i	0.720116	+	0.693854i	$0.244089\pi$
$853$			40.5296i			1.38771i	−0.720116	+	0.693854i	$0.755911\pi$
$854$	−1.52119	−	0.820654i	−0.0520542	−	0.0280822i
$855$	11.9143			0.407461
$856$	3.59281	+	41.3822i	0.122800	+	1.41441i
$857$	5.61531			0.191815			0.0959076	−	0.995390i	$-0.469425\pi$
$857$	5.61531			0.191815			0.0959076	+	0.995390i	$0.469425\pi$
$858$	0.489289	+	0.263962i	0.0167040	+	0.00901150i
$859$		−	27.4721i		−	0.937335i	−0.883375	−	0.468668i	$-0.844734\pi$
$859$		−	27.4721i		−	0.937335i	0.883375	−	0.468668i	$-0.155266\pi$
$860$	7.50367	+	11.4198i	0.255873	+	0.389411i
$861$		−	0.136959i		−	0.00466754i
$862$	12.6837	−	23.5110i	0.432010	−	0.800789i
$863$	42.8898			1.45998			0.729992	−	0.683456i	$-0.239524\pi$
$863$	42.8898			1.45998			0.729992	+	0.683456i	$0.239524\pi$
$864$	3.88631	−	3.06592i	0.132215	−	0.104305i
$865$	6.58546			0.223912
$866$	−14.7002	+	27.2489i	−0.499534	+	0.925954i
$867$			2.34185i			0.0795333i
$868$	0.211250	+	0.321500i	0.00717031	+	0.0109124i
$869$			40.3847i			1.36996i
$870$	0.800307	+	0.431750i	0.0271329	+	0.0146377i
$871$	−8.29273			−0.280988
$872$	−3.61213	−	41.6047i	−0.122322	−	1.40891i
$873$	−30.8291			−1.04341
$874$	−33.2860	−	17.9572i	−1.12592	−	0.607410i
$875$			1.31729i			0.0445325i
$876$	1.70727	−	1.12181i	0.0576833	−	0.0379023i
$877$			31.7005i			1.07045i	0.844709	+	0.535226i	$0.179773\pi$
$877$			31.7005i			1.07045i	−0.844709	+	0.535226i	$0.820227\pi$
$878$	9.27131	−	17.1856i	0.312891	−	0.579986i
$879$	1.58187			0.0533551
$880$	−4.26396	+	9.86098i	−0.143738	+	0.332414i
$881$	−44.4011			−1.49591			−0.747955	−	0.663749i	$-0.768964\pi$
$881$	−44.4011			−1.49591			−0.747955	+	0.663749i	$0.768964\pi$
$882$	−13.9572	+	25.8715i	−0.469962	+	0.871137i
$883$			1.28287i			0.0431719i	0.999767	+	0.0215859i	$0.00687155\pi$
$883$			1.28287i			0.0431719i	−0.999767	+	0.0215859i	$0.993128\pi$
$884$	1.67146	−	1.09828i	0.0562173	−	0.0369391i
$885$			1.80765i			0.0607636i
$886$	31.8325	+	17.1730i	1.06943	+	0.576939i
$887$	41.5212			1.39415			0.697073	−	0.717001i	$-0.254486\pi$
$887$	41.5212			1.39415			0.697073	+	0.717001i	$0.254486\pi$
$888$	−1.64090	+	0.142463i	−0.0550648	+	0.00478074i
$889$	0.892886			0.0299464
$890$	6.68585	+	3.60688i	0.224110	+	0.120903i
$891$			23.6560i			0.792506i
$892$	−7.82517	−	11.9091i	−0.262006	−	0.398745i
$893$		−	28.4998i		−	0.953708i
$894$	−1.17513	+	2.17827i	−0.0393024	+	0.0728523i
$895$	7.56090			0.252733
$896$	−0.523299	+	1.57108i	−0.0174822	+	0.0524860i
$897$	−0.978577			−0.0326737
$898$	−16.3215	+	30.2541i	−0.544656	+	1.00959i
$899$		−	5.77323i		−	0.192548i
$900$	−13.0852	−	19.9143i	−0.436174	−	0.663810i
$901$		−	8.97858i		−	0.299120i
$902$	−21.3717	−	11.5296i	−0.711600	−	0.383894i
$903$	0.146365			0.00487074
$904$	−11.1506	+	0.968095i	−0.370863	+	0.0321984i
$905$	−0.628308			−0.0208857
$906$	−2.32988	−	1.25692i	−0.0774050	−	0.0417585i
$907$			41.9834i			1.39404i	0.717054	+	0.697018i	$0.245490\pi$
$907$			41.9834i			1.39404i	−0.717054	+	0.697018i	$0.754510\pi$
$908$	41.6791	−	27.3864i	1.38317	−	0.908849i
$909$			53.4868i			1.77404i
$910$	−0.0982788	+	0.182173i	−0.00325791	+	0.00603898i
$911$	−37.5443			−1.24390			−0.621949	−	0.783058i	$-0.713659\pi$
$911$	−37.5443			−1.24390			−0.621949	+	0.783058i	$0.713659\pi$
$912$	−0.929460	+	2.14950i	−0.0307775	+	0.0711771i
$913$	−11.5296			−0.381575
$914$	8.19235	−	15.1856i	0.270979	−	0.502296i
$915$		−	1.22219i		−	0.0404044i
$916$	4.94277	−	3.24778i	0.163314	−	0.107310i
$917$		−	2.17092i		−	0.0716902i
$918$	−1.08914	−	0.587567i	−0.0359468	−	0.0193926i
$919$	48.7005			1.60648			0.803241	−	0.595654i	$-0.203107\pi$
$919$	48.7005			1.60648			0.803241	+	0.595654i	$0.203107\pi$
$920$	−1.63565	−	18.8396i	−0.0539259	−	0.621122i
$921$	0.722421			0.0238046
$922$	9.98382	+	5.38608i	0.328800	+	0.177381i
$923$			5.51806i			0.181629i
$924$	0.0631933	+	0.0961734i	0.00207891	+	0.00316387i
$925$			15.9143i			0.523259i
$926$	−24.2113	+	44.8788i	−0.795631	+	1.47481i
$927$	30.5301			1.00274
$928$	19.5107	−	15.3920i	0.640470	−	0.505268i
$929$	−11.1281			−0.365100			−0.182550	−	0.983197i	$-0.558435\pi$
$929$	−11.1281			−0.365100			−0.182550	+	0.983197i	$0.558435\pi$
$930$	−0.129153	+	0.239403i	−0.00423511	+	0.00785034i
$931$		−	27.9143i		−	0.914855i
$932$	5.70264	+	8.67881i	0.186796	+	0.284284i
$933$		−	0.115077i		−	0.00376745i
$934$	−23.8793	−	12.8824i	−0.781354	−	0.421525i
$935$	2.68585			0.0878366
$936$	−0.728692	−	8.39312i	−0.0238180	−	0.274338i
$937$	17.6153			0.575467			0.287733	−	0.957711i	$-0.407098\pi$
$937$	17.6153			0.575467			0.287733	+	0.957711i	$0.407098\pi$
$938$	−1.51071	−	0.815000i	−0.0493265	−	0.0266107i
$939$			2.03971i			0.0665634i
$940$	11.9091	−	7.82517i	0.388431	−	0.255229i
$941$		−	35.6577i		−	1.16241i	−0.813758	−	0.581204i	$-0.802582\pi$
$941$		−	35.6577i		−	1.16241i	0.813758	−	0.581204i	$-0.197418\pi$
$942$	−2.13481	+	3.95715i	−0.0695558	+	0.128931i
$943$	42.7434			1.39192
$944$	45.3435	+	19.6069i	1.47581	+	0.638150i
$945$	0.128078			0.00416638
$946$	12.3215	−	22.8396i	0.400607	−	0.742578i
$947$			22.7715i			0.739976i	0.929037	+	0.369988i	$0.120638\pi$
$947$			22.7715i			0.739976i	−0.929037	+	0.369988i	$0.879362\pi$
$948$	−3.67850	+	2.41706i	−0.119472	+	0.0785024i
$949$		−	6.97858i		−	0.226534i
$950$	19.9143	+	10.7434i	0.646105	+	0.348561i
$951$	−2.92104			−0.0947212
$952$	0.412433	−	0.0358075i	0.0133670	−	0.00116053i
$953$	−1.74338			−0.0564738			−0.0282369	−	0.999601i	$-0.508989\pi$
$953$	−1.74338			−0.0564738			−0.0282369	+	0.999601i	$0.508989\pi$
$954$	−33.2860	−	17.9572i	−1.07767	−	0.581384i
$955$			10.1004i			0.326841i
$956$	15.8111	+	24.0628i	0.511367	+	0.778246i
$957$		−	1.72700i		−	0.0558260i
$958$	−7.99789	+	14.8252i	−0.258400	+	0.478980i
$959$	−1.42923			−0.0461523
$960$	−1.15340	+	0.201799i	−0.0372259	+	0.00651302i
$961$	−29.2730			−0.944290
$962$	−2.67146	+	4.95191i	−0.0861314	+	0.159656i
$963$		−	43.7429i		−	1.40960i
$964$	−25.6216	−	38.9933i	−0.825215	−	1.25589i
$965$			3.37169i			0.108539i
$966$	−0.178270	−	0.0961734i	−0.00573575	−	0.00309433i
$967$	−33.8402			−1.08823			−0.544113	−	0.839012i	$-0.683134\pi$
$967$	−33.8402			−1.08823			−0.544113	+	0.839012i	$0.683134\pi$
$968$	−10.6689	+	0.926280i	−0.342913	+	0.0297718i
$969$	0.585462			0.0188077
$970$	12.8824	+	6.94981i	0.413629	+	0.223145i
$971$			40.0031i			1.28376i	0.766804	+	0.641881i	$0.221846\pi$
$971$			40.0031i			1.28376i	−0.766804	+	0.641881i	$0.778154\pi$
$972$	−6.54262	+	4.29900i	−0.209855	+	0.137891i
$973$			2.85050i			0.0913828i
$974$	−10.6472	+	19.7360i	−0.341159	+	0.632383i
$975$	0.585462			0.0187498
$976$	−30.6577	−	13.2566i	−0.981329	−	0.424334i
$977$	38.7005			1.23814			0.619070	−	0.785336i	$-0.287510\pi$
$977$	38.7005			1.23814			0.619070	+	0.785336i	$0.287510\pi$
$978$	−2.02877	+	3.76060i	−0.0648729	+	0.120251i
$979$		−	14.4275i		−	0.461106i
$980$	11.6644	−	7.66442i	0.372606	−	0.244831i
$981$			43.9781i			1.40411i
$982$	4.86802	+	2.62620i	0.155345	+	0.0838055i
$983$	23.8536			0.760813			0.380406	−	0.924819i	$-0.375784\pi$
$983$	23.8536			0.760813			0.380406	+	0.924819i	$0.375784\pi$
$984$	−0.228921	−	2.63673i	−0.00729775	−	0.0840559i
$985$	−14.7220			−0.469081
$986$	−5.46787	−	2.94981i	−0.174132	−	0.0939410i
$987$		−	0.152637i		−	0.00485848i
$988$	4.39312	+	6.68585i	0.139764	+	0.212705i
$989$			45.6791i			1.45251i
$990$	5.37169	−	9.95715i	0.170724	−	0.316459i
$991$	−3.01300			−0.0957111			−0.0478556	−	0.998854i	$-0.515239\pi$
$991$	−3.01300			−0.0957111			−0.0478556	+	0.998854i	$0.515239\pi$
$992$	4.60437	+	5.83642i	0.146189	+	0.185307i
$993$	1.71354			0.0543776
$994$	−0.542308	+	1.00524i	−0.0172010	+	0.0318843i
$995$			13.6644i			0.433191i
$996$	−0.690057	−	1.05019i	−0.0218653	−	0.0332766i
$997$			7.13650i			0.226015i	0.993594	+	0.113008i	$0.0360484\pi$
$997$			7.13650i			0.226015i	−0.993594	+	0.113008i	$0.963952\pi$
$998$	−28.8500	−	15.5640i	−0.913232	−	0.492671i
$999$	3.48148			0.110149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.b.c.53.5	✓	6
3.2	odd	2		936.2.g.c.469.2		6
4.3	odd	2		416.2.b.c.209.4		6
8.3	odd	2		416.2.b.c.209.3		6
8.5	even	2	inner	104.2.b.c.53.6	yes	6
12.11	even	2		3744.2.g.c.1873.5		6
16.3	odd	4		3328.2.a.bg.1.2		3
16.5	even	4		3328.2.a.bh.1.2		3
16.11	odd	4		3328.2.a.bf.1.2		3
16.13	even	4		3328.2.a.be.1.2		3
24.5	odd	2		936.2.g.c.469.1		6
24.11	even	2		3744.2.g.c.1873.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.c.53.5	✓	6	1.1	even	1	trivial
104.2.b.c.53.6	yes	6	8.5	even	2	inner
416.2.b.c.209.3		6	8.3	odd	2
416.2.b.c.209.4		6	4.3	odd	2
936.2.g.c.469.1		6	24.5	odd	2
936.2.g.c.469.2		6	3.2	odd	2
3328.2.a.be.1.2		3	16.13	even	4
3328.2.a.bf.1.2		3	16.11	odd	4
3328.2.a.bg.1.2		3	16.3	odd	4
3328.2.a.bh.1.2		3	16.5	even	4
3744.2.g.c.1873.2		6	24.11	even	2
3744.2.g.c.1873.5		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.671462 - 1.24464i) q^{2} -0.146365i q^{3} +(-1.09828 - 1.67146i) q^{4} -1.00000i q^{5} +(-0.182173 - 0.0982788i) q^{6} -0.146365 q^{7} +(-2.81783 + 0.244644i) q^{8} +2.97858 q^{9} +(-1.24464 - 0.671462i) q^{10} +2.68585i q^{11} +(-0.244644 + 0.160750i) q^{12} +1.00000i q^{13} +(-0.0982788 + 0.182173i) q^{14} -0.146365 q^{15} +(-1.58757 + 3.67146i) q^{16} +1.00000 q^{17} +(2.00000 - 3.70727i) q^{18} +4.00000i q^{19} +(-1.67146 + 1.09828i) q^{20} +0.0214229i q^{21} +(3.34292 + 1.80344i) q^{22} -6.68585 q^{23} +(0.0358075 + 0.412433i) q^{24} +4.00000 q^{25} +(1.24464 + 0.671462i) q^{26} -0.875057i q^{27} +(0.160750 + 0.244644i) q^{28} -4.39312i q^{29} +(-0.0982788 + 0.182173i) q^{30} +1.31415 q^{31} +(3.50367 + 4.44120i) q^{32} +0.393115 q^{33} +(0.671462 - 1.24464i) q^{34} +0.146365i q^{35} +(-3.27131 - 4.97858i) q^{36} +3.97858i q^{37} +(4.97858 + 2.68585i) q^{38} +0.146365 q^{39} +(0.244644 + 2.81783i) q^{40} -6.39312 q^{41} +(0.0266638 + 0.0143846i) q^{42} -6.83221i q^{43} +(4.48929 - 2.94981i) q^{44} -2.97858i q^{45} +(-4.48929 + 8.32150i) q^{46} -7.12494 q^{47} +(0.537375 + 0.232365i) q^{48} -6.97858 q^{49} +(2.68585 - 4.97858i) q^{50} -0.146365i q^{51} +(1.67146 - 1.09828i) q^{52} -8.97858i q^{53} +(-1.08914 - 0.587567i) q^{54} +2.68585 q^{55} +(0.412433 - 0.0358075i) q^{56} +0.585462 q^{57} +(-5.46787 - 2.94981i) q^{58} -12.3503i q^{59} +(0.160750 + 0.244644i) q^{60} +8.35027i q^{61} +(0.882404 - 1.63565i) q^{62} -0.435961 q^{63} +(7.88030 - 1.37873i) q^{64} +1.00000 q^{65} +(0.263962 - 0.489289i) q^{66} +8.29273i q^{67} +(-1.09828 - 1.67146i) q^{68} +0.978577i q^{69} +(0.182173 + 0.0982788i) q^{70} +5.51806 q^{71} +(-8.39312 + 0.728692i) q^{72} -6.97858 q^{73} +(4.95191 + 2.67146i) q^{74} -0.585462i q^{75} +(6.68585 - 4.39312i) q^{76} -0.393115i q^{77} +(0.0982788 - 0.182173i) q^{78} +15.0361 q^{79} +(3.67146 + 1.58757i) q^{80} +8.80765 q^{81} +(-4.29273 + 7.95715i) q^{82} +4.29273i q^{83} +(0.0358075 - 0.0235283i) q^{84} -1.00000i q^{85} +(-8.50367 - 4.58757i) q^{86} -0.643000 q^{87} +(-0.657077 - 7.56825i) q^{88} -5.37169 q^{89} +(-3.70727 - 2.00000i) q^{90} -0.146365i q^{91} +(7.34292 + 11.1751i) q^{92} -0.192347i q^{93} +(-4.78412 + 8.86802i) q^{94} +4.00000 q^{95} +(0.650039 - 0.512817i) q^{96} -10.3503 q^{97} +(-4.68585 + 8.68585i) q^{98} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} - 10 q^{6} + 2 q^{7} - 8 q^{8} - 12 q^{9} + 6 q^{12} + 4 q^{14} + 2 q^{15} + 10 q^{16} + 6 q^{17} + 12 q^{18} - 4 q^{20} + 8 q^{22} - 16 q^{23} + 12 q^{24} + 24 q^{25} - 20 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 - 10 * q^6 + 2 * q^7 - 8 * q^8 - 12 * q^9 + 6 * q^12 + 4 * q^14 + 2 * q^15 + 10 * q^16 + 6 * q^17 + 12 * q^18 - 4 * q^20 + 8 * q^22 - 16 * q^23 + 12 * q^24 + 24 * q^25 - 20 * q^28 + 4 * q^30 + 32 * q^31 - 12 * q^32 - 16 * q^33 - 2 * q^34 + 16 * q^36 - 2 * q^39 - 6 * q^40 - 20 * q^41 - 28 * q^42 + 12 * q^44 - 12 * q^46 - 10 * q^47 - 10 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 + 38 * q^54 - 8 * q^55 + 22 * q^56 - 8 * q^57 + 12 * q^58 - 20 * q^60 - 28 * q^62 - 44 * q^63 + 22 * q^64 + 6 * q^65 + 32 * q^66 - 2 * q^68 + 10 * q^70 - 18 * q^71 - 32 * q^72 - 12 * q^73 + 28 * q^74 + 16 * q^76 - 4 * q^78 - 12 * q^79 + 16 * q^80 + 46 * q^81 - 20 * q^82 + 12 * q^84 - 18 * q^86 + 80 * q^87 - 16 * q^88 + 16 * q^89 - 28 * q^90 + 32 * q^92 + 24 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98

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